AP EAMCET202315 May 2023Morning ShiftMathematicsContinuity and DifferentiabilityActual

Let f(x) be a real valued function. If f^ (x) is a constant for all x R , f(0)=2 and f^ (0)=1 , then

Options

Af ( x ) is not continuous on R
Bf(x) is continuous at x=0,1,2 and 3 only
Cf(x) is continuous only on [0, )
Df ( x ) is continuous on R

Correct answer

D. f ( x ) is continuous on R

Step-by-step solution

Since f^ (x) is a constant f^ (x)=a (say) ...(1) f(x)=a x+b where b is arbitrary constant. ...(2) Since f(0)=2 b=2 Since f^ (0)=1 a=1 f(x)=(x+2) Which is continuous on (- , ) i.e R

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