Question

Find the derivative of x 2 – 2 at x = 10.

Answer 1

Let the given function be:

f( x )=( x 2 −2 )

The derivative of the given function at x=10

From the definition, derivative of a function, f( x ) over a point a can be written as:

f ' ( x )= lim h→0 f( x+h )−f ( a ) h

Here, the value of a=10 ,

On solving the value of f ' ( x ) , we get

f ' ( x )= lim h→0 f( 10+h )−f( 10 ) h = lim h→0 [ ( 10+h ) 2 −2 ]−( 10 2 −2 ) h = lim h→0 10 2 +2⋅10⋅h+ h 2 −2− 10 2 +2 h = lim h→0 20h+ h 2 h

Taking h common from numerator and denominator:

f ' ( x )= lim h→0 20+h =20+0 =20

Thus, the derivative of the function f( x )=( x 2 −2 ) at x=10 is 20.