WB JEE 2019 | Limits, Continuity and Differentiability Question 54 | Mathematics

WB JEE 2019

MCQ (More than One Correct Answer)

-0.25

Let $$f:[1,3] \to R$$ be a continuous function that is differentiable in (1, 3) an

f'(x) = | f(x) |² + 4 for all x$$ \in $$ (1, 3). Then,

f(3) $$-$$ f(1) = 5 is true

f(3) $$-$$ f(1) = 5 is false

f(3) $$-$$ f(1) = 7 is false

f(3) $$-$$ f(1) > 0 only at one point of (1, 3)

WB JEE 2019

MCQ (More than One Correct Answer)

-0

Consider the function $$f(x) = {{{x^3}} \over 4} - \sin \pi x + 3$$

f(x) does not attain value within the interval [$$-$$2, 2]

f(x) takes on the value $$2{1 \over 3}$$ in the interval [$$-$$2, 2]

f(x) takes on the value $$3{1 \over 4}$$ in the interval [$$-$$2, 2]

f(x) takes no value p, 1 < p < 5 in the interval [$$-$$2, 2].

WB JEE 2017

MCQ (More than One Correct Answer)

-0

Let f : R $$ \to $$ R be twice continuously differentiable. Let f(0) = f(1) = f'(0) = 0. Then,

f''(x) $$ \ne $$ 0 for all x

f''(c) = 0 for some c $$ \in $$ R

f''(x) $$ \ne $$ 0 if x $$ \ne $$ 0

f'(x) > 0 for all x

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