Question

The value of derivative at the point x=−2 on the curve y=x2 is equal to .

A
-4
B
4
C
-2
D
2

Solution

The correct option is A -4We know that as per the first principle, the derivative of a function is given by f′(x)=limh→0f(x+h)−f(x)h f(x+h)=(x+h)2=x2+h2+2hxf(x)=x2 So f′(x)=limh→0x2+h2+2hx−x2h=limh→0h2+2hxh=limh→0h(h+2x)h=2x At x = -2, f'(x)= 2 × (-2) = -4

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