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Find the absolute minimum and absolute maximum of f(x)=x^1/3(7-x)^2 on [-1,7].

Related Topics

Wize University Calculus 1 Textbook > Applications of Differentiation

Maximum and Minimum on Closed Intervals

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Find the absolute minimum and absolute maximum of f(x)=x13(7−x)2 f\left(x\right)=x^{\frac{1}{3}}\left(7-x\right)^2\ on [−1,7]\left[-1,7\right].


More Maximum and Minimum on Closed Intervals Questions:
Maximum and Minimum on Closed Intervals
Find the absolute max of the function f(x)=cos⁡x⋅e−xf\left(x\right)=\cos x\cdot e^{-x} on [0,π]\left[0,\pi\right]
Closed Intervals: Maximum and Minimum
Find the local and absolute extreme values of f(x)=3x−4x2+1f(x)=\frac{3x-4}{x^2+1} on the interval [−2,2][-2,2]
Relative Extrema
Find and classify all local and absolute extrema of f(x)=sin⁡xcos⁡xf\left(x\right)=\sin x\cos x on the interval [0,  2π]\left[0,\ \ 2\pi\right].
Concavity and Inflection Points: Graph of a Derivative
Practice: Graph of a Derivative
Suppose that ff is a differentiable function on the interval [−4,2]\left[-4,2\right]. If the following graph represents the derivative of ff, which of the following statements is correct?
Determine where the absolute extrema of f(x)=3x23−2xf(x)=3x^{\frac{2}{3}}-2x on the interval [−1,1] [-1,1] occur, and their values.
Practice: Absolute Extrema on Closed Interval
Q.\textbf{Q.} Find the absolute maximum and minimum values of f(x)=6x43−3x13\displaystyle f(x)=6x^{\frac{4}{3}}-3x^{\frac{1}{3}} on the interval [−1,1][-1,1] and then everywhere, using the second derivative test.
Practice: Relative Extrema with Trig
Q.\textbf{Q.} Find all the relative extrema of f(x)=2ex(sin⁡x−cos⁡x)\displaystyle f(x)=2e^x(\sin{x}-\cos{x}) on the interval [π2,π]\bigg[\dfrac{\pi}{2},\pi\bigg].
Q.\textbf{Q.} Find the absolute extrema of f(x)=2xx2+1\displaystyle f(x)=\frac{2x}{x^2+1} on the interval [0,2][0,2]. Then find the local/absolute extrema on its domain, and intervals of increase and decrease.
Practice: Graph of a Derivative (~F2018 Final Q17) (~F2016 Final Q16)
Practice: Graph of a Derivative
Suppose that ff is a differentiable function on the interval (−4,2)(-4,2). If the following graph represents the derivative of ff, which of the following statements is correct?
Maximum and Minimum on Closed Intervals
Find the absolute max of the function f(x)=cos⁡x⋅e−xf\left(x\right)=\cos x\cdot e^{-x} on [0,π]\left[0,\pi\right]
Critical Points and Extrema: Maximum and Minimum on Closed Intervals
Find the absolute maximum of value of f(x)=2xx2+1\displaystyle f(x)=\frac{2x}{x^2+1}
on the interval [0,2][0,2].
Critical points and extrema: Maximum and minimum on closed intervals
Find the absolute maximum value of f(x)=2ex(sin⁡x−cos⁡x)f(x)=2e^x(\sin x-\cos x)
on the interval [π/2,π][\pi/2,\pi].
Critical points and extrema: Maximum and Minimum on closed intervals
Find the absolute minimum of f(x)=arcsin(x2)f(x)=\text{arcsin}\left(\frac{x}{2}\right) on the interval [1,2][1,2].
Relative Extrema
Find and classify all local and absolute extrema of f(x)=sin⁡xcos⁡xf\left(x\right)=\sin x\cos x on the interval [0,  2π]\left[0,\ \ 2\pi\right].
Find the absolute maximum value of f(x)=2ex(sin⁡x−cos⁡x)f(x)=2e^x(\sin x-\cos x)
on the interval [π/2,π][\pi/2,\pi].
Practice: Relative Extrema
Practice Question: Relative Extrema
Find and classify all local and absolute extrema of f(x)=sin⁡xcos⁡xf\left(x\right)=\sin x\cos x on the interval [0,  2π]\left[0,\ \ 2\pi\right].
Closed Intervals: Maximum and Minimum
Find the local and absolute extreme values of f(x)=3x−4x2+1f(x)=\frac{3x-4}{x^2+1} on the interval [−2,2][-2,2]
The absolute maximum value of f(x)=1−x23x+5f(x)=\dfrac{1-x^2}{3x+5} , over the closed interval [−1,2][-1,2] is:
final114
The absolute maximum value of f(x)=1−x23x+5f(x)=\dfrac{1-x^2}{3x+5} , over the closed interval [−1,2][-1,2] is:
final114
The absolute maximum value of f(x)=1−x23x+5f(x)=\dfrac{1-x^2}{3x+5} , over the closed interval [−1,2][-1,2] is:
Find the absolute minimum of f(x)=arcsin(x2)f(x)=\text{arcsin}\left(\frac{x}{2}\right) on the interval [1,2][1,2].
Practice: Absolute Extrema on Closed Interval
Q.\textbf{Q.} Find the absolute maximum and minimum values of f(x)=6x43−3x13\displaystyle f(x)=6x^{\frac{4}{3}}-3x^{\frac{1}{3}} on the interval [−1,1][-1,1] and then everywhere, using the second derivative test.
Practice: Relative Extrema with Trig
Q.\textbf{Q.} Find all the relative extrema of f(x)=2ex(sin⁡x−cos⁡x)\displaystyle f(x)=2e^x(\sin{x}-\cos{x}) on the interval [π2,π]\bigg[\dfrac{\pi}{2},\pi\bigg].
Q.\textbf{Q.} Find the absolute extrema of f(x)=2xx2+1\displaystyle f(x)=\frac{2x}{x^2+1} on the interval [0,2][0,2]. Then find the local/absolute extrema on its domain, and intervals of increase and decrease.
Determine where the absolute extrema of f(x)=3x23−2xf(x)=3x^{\frac{2}{3}}-2x on the interval [−1,1] [-1,1] occur, and their values.
The absolute maximum value of f(x)=1−x23x+5f(x)=\dfrac{1-x^2}{3x+5} , over the closed interval [−1,2][-1,2] is:
Find the absolute minimum and absolute maximum of f(x)=x13(7−x)2  on [−1,7]f\left(x\right)=x^{\frac{1}{3}}\left(7-x\right)^2\ \text{ on }\left[-1,7\right].
For the following function, determine all the local and global minimum/maximum and inflection points over the given interval
h(x)=x5−x3+1over [−2,2]h(x)= x^5-x^3+1\quad \text{over}\ [-2,2]
For the following function, determine all the local and global minimum/maximum and inflection points over the given interval
f(x)=x3−3x2 over  [−1,3]f(x)=x^3-3x^2\quad \text{ over }\ [-1,3]
Find the absolute maximum of value of f(x)=2xx2+1\displaystyle f(x)=\frac{2x}{x^2+1} on the interval [0,2][0,2].
Find the absolute minimum and absolute maximum of f(x)=x13(7−x)2 f\left(x\right)=x^{\frac{1}{3}}\left(7-x\right)^2\ on [−1,7]\left[-1,7\right].
Concavity and Inflection Points: Graph of a Derivative
Practice: Graph of a Derivative
Suppose that ff is a differentiable function on the interval [−4,2]\left[-4,2\right]. If the following graph represents the derivative of ff, which of the following statements is correct?