﻿    If f is differentiable for all x then  : Kaysons Education

# If f is Differentiable For All x then

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## Question

### Solution

Correct option is

a = 3/4, b = 9/4

Since f is differentiable for all x, in particular it is continuous at 2. But (2) = 4a – 2b + 3 and  so 4a – 2b + 3 = 2a

i.e. 2a – 2b + 3 = 0                    …(i)

Also f’(2) = a and f’(2+)

Thus 4a – b = a ⇒ 3a = b               …(ii)

Solving (i) and (ii) a = 3/4 and b = 9/4.

#### SIMILAR QUESTIONS

Q1

If f’ is differentiable function and f’’(x) is continuous at x = 0 and f’’(0) =a, the value of

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Q3

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Q5

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Q7

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Q9

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Q10

Let f and g be differentiable function such that f’(x) = 2g(x) and g’(x) = –f(x), and let T(x) = (f (x))2 – (g(x))2. Then T’(x) is equal to