Instantaneous Rate of Change & the Tangent Line

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Practice: Instantaneous Rate of Change & the Tangent Line
Let f(x)=x2+x+1f(x)=x^2+x+1f(x)=x2+x+1. Determine the instantaneous rate of change for each interval to the nearest hundredth. 

~0\leq{}x\leq{}1

~0.5\leq{}x\leq{}1

~0.9\leq{}x\leq{}1

~0.99\leq{}x\leq{}1

1\leq{}x\leq{}2

1\leq{}x\leq{}1.5

1\leq{}x\leq{}1.1

1\leq{}x\leq{}1.01

I don't know

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Instantaneous Rate of Change & the Tangent Line

Practice: Instantaneous Rate of Change & the Tangent Line
A soccer ball is being inflated for a tournament. Estimate how fast the area of the ball is changing using the difference quotient when the radius is 555cm and allowing h=0.001h=0.001h=0.001. 

Instantaneous Rate of Change & the Tangent Line

Practice: Instantaneous Rate of Change & the Tangent Line∫
A cylindrical pot is being filled with water. Estimate how fast the volume of water is changing if the radius of the pot is 30cm, the height of the pot is 40cm and allow h=0.001h=0.001h=0.001. Use the difference quotient.

Instantaneous Rate of Change & the Tangent Line

Practice: Instantaneous Rate of Change & the Tangent Line
An investment builds interest annually and is modeled by the function P=1050(1.02)tP=1050(1.02)^tP=1050(1.02)t. Estimate the instantaneous rate of change using the difference quotient at t=10t=10t=10 for the following value of hhh. Round answers to the nearest hundredth when required.  

Instantaneous Rate of Change & the Tangent Line

Practice: Instantaneous Rate of Change & the Tangent Line
A soccer ball is kicked into the air and the projectile is modelled by the function d(t)=−9.8t2+19.8t+2d(t)=-9.8t^2+19.8t+2d(t)=−9.8t2+19.8t+2. Estimate the instantaneous rate of change using the difference quotient at t=5t=5t=5 for the following value of hhh. Round answers to the nearest hundredth when required.  

Instantaneous Rate of Change & the Tangent Line

Practice: Instantaneous Rate of Change & the Tangent Line
Let f(x)=2x2+3xf(x)=2x^2+3xf(x)=2x2+3x. Determine the instantaneous rate of change for each interval to the nearest hundredth. 

Instantaneous Rate of Change & the Tangent Line

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Instantaneous Rate of Change & the Tangent Line

Practice: Instantaneous Rate of Change & the Tangent Line

More Instantaneous Rate of Change & the Tangent Line Questions:

Instantaneous Rate of Change & the Tangent Line

Instantaneous Rate of Change & the Tangent Line

Instantaneous Rate of Change & the Tangent Line

Instantaneous Rate of Change & the Tangent Line

Instantaneous Rate of Change & the Tangent Line