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India
Class XI

The Derivative as a Limit - Limiting Chord Process

Interactive practice questions

Consider the function $f\left(x\right)=2x^2$f(x)=2x2

a

By filling in the table of values, complete the limiting chord process for $f\left(x\right)=2x^2$f(x)=2x2 at the point $x=1$x=1.

$a$a $b$b $h=b-a$h=ba $\frac{f\left(b\right)-f\left(a\right)}{b-a}$f(b)f(a)ba
$1$1 $2$2 $1$1 $\editable{}$
$1$1 $1.5$1.5 $\editable{}$ $\editable{}$
$1$1 $1.1$1.1 $\editable{}$ $\editable{}$
$1$1 $1.05$1.05 $\editable{}$ $\editable{}$
$1$1 $1.01$1.01 $\editable{}$ $\editable{}$
$1$1 $1.001$1.001 $\editable{}$ $\editable{}$
$1$1 $1.0001$1.0001 $\editable{}$ $\editable{}$
b

The instantaneous rate of change of $f\left(x\right)$f(x) at $x=1$x=1 is:

Easy
7min

Consider the function $f\left(x\right)=x^2$f(x)=x2

Easy
6min

Consider the function $f\left(x\right)=4^x$f(x)=4x

Easy
7min

Consider the function $f\left(x\right)=-x^2+5$f(x)=x2+5

Medium
6min
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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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