Application of Derivatives - Online Test
Q1. Find the slope of the normal to the curve at
Answer : Option B
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Q2. The function f (x) = has a
Answer : Option A
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Q3. The minimum value of f(x) =sin x cos x is
Answer : Option B
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Q4. The maximum value of is
Answer : Option A
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Q5. The function f (x) = | x | has
Answer : Option A
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Q6. If a differentiable function f (x) has a relative minimum at x = 0, then the function y = f (x) + a x + b has a relative minimum at x = 0 for
Answer : Option B
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Q7. Let f (x) be differentiable in (0, 4) and f (2) = f (3) and S = {c : 2 < c < 3, f’ (c) = 0 } then
Answer : Option D
Explaination / Solution:
Since given f(x) is differentiable in (2,3) and f(2) = f(3) we have conditions of Rolle′s Theorem are satisfied by f(x) in [2,3]. Hence there exist atleast one real c in (2,3) s.t.f′
(c) = 0. Therefore, the set S contains atleast one element.
Q8. Rolle’s Theorem is not applicable to the function f(x) = | x | for −2⩽x⩽2 because
Answer : Option C
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Q9.
Find the approximate value of f(2.01) where
Answer : Option B
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Q10. Find the approximate value of f(5.001) where
Answer : Option A
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