Test Index

MHTCET 16 May 2024 Shift 1 Paper

Question : 145 of 150

Marks: +1, -0

f(1)=1, f^{\prime}(1)=5

\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f}(x))^{2}

x=1

Solution:

Concept:

Use the chain rule for composite functions and substitute the given values.

Explanation:

Let

y = f(f(f(x))) + (f(x))^2

Differentiate with respect to

x

\frac{dy}{dx} = f'(f(f(x))) \cdot f'(f(x)) \cdot f'(x) + 2 f(x) f'(x)

x = 1

, we use

f(1) = 1

and

f'(1) = 5

Since

f(f(f(1))) = f(f(1)) = f(1) = 1

, the first term becomes

f'(1) \cdot f'(1) \cdot f'(1)

Thus,

\left.\frac{dy}{dx}\right|_{x=1} = 5 \cdot 5 \cdot 5 + 2 \cdot 1 \cdot 5

= 125 + 10 = 135

Answer:

The derivative of the given expression at

x = 1

135

So, the correct option is C.

Go to Question:

Prev Question

Next Question