People living at Mars define the derivative of in an unusual manner as where denotes…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

People living at Mars define the derivative of

f(x)

in an unusual manner as

D^*f(x)=\lim_{h\to 0}\frac{f^2(x+h)-f^2(x)}{h}

where

D^*f(x)

denotes the derivative of

f(x)

at Mars. The value of

D^*f(x)

at the point on the curve

y=f(x)

such that tangent to it are parallel to

x

-axis is (a) zero (b)

f(x)

(c)

2f(x)

(d)

x f(x)

Related theory

Differentiation Rules
Derivative Foundations
Differentiation from first principles
Derivatives
Limits and Derivatives

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