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India
Class XI

Average Vs Instantaneous Rates of Change

Interactive practice questions

Consider the function $f\left(x\right)=2$f(x)=2 drawn below.

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a

Calculate the average rate of change between $x=3$x=3 and $x=6$x=6.

b

State the gradient of the tangent at the point $x=3$x=3.

Easy
< 1min

Consider the function $f\left(x\right)=2x+3$f(x)=2x+3 drawn below.

Easy
1min

Consider the function $f\left(x\right)=-\frac{\left(x-8\right)^2}{3}+7$f(x)=(x8)23+7.

Easy
2min

Consider the function $f\left(x\right)=-\frac{\left(x-4\right)^2}{2}+6$f(x)=(x4)22+6.

Medium
2min
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Outcomes

11.C.LD.1

Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit. Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

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