Q21Written answer
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Given,
Therefore, f(x) is differentiable at x = 0
NCERT Exemplar · Class 12 · Maths
Chapter 5: Continuity and Differentiability
Practice each question, then open the answer or worked solution.
Short Answer (S.A.)
53 questionsQ22Written answer
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We know that, f(x) is differentiable at x = 2 if
Thus, f(x) is not differentiable at x = 2.
Q23Written answer
Show that f (x) = |x – 5| is continuous but not differentiable at x = 5.
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Therefore, f(x) is not differentiable at x = 5.
Q24Written answer
A function f : R ® R satisfies the equation f ( x + y) = f (x) f (y) for all x, y ÎR, f (x) ¹ 0. Suppose that the function is differentiable at x = 0 and f ¢ (0) = 2. Prove that f ¢(x) = 2 f (x).
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Given,
f : R ® R satisfies the equation f ( x + y) = f (x) f (y) for all x, y ÎR, f (x) ¹ 0
Let us take any point x = 0 at which the function f(x) is differentiable.
Therefore, f’(x) = 2f(x).
Differentiate each of the following w.r.t. x (Exercises 25 to 43) :
Q25Written answer
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Q28Written answer
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Q30Written answer
sinn (ax2 + bx + c)
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