Manipal MET2016MathematicsApplication of Derivatives

Let h(x)= (x, x^2 ) , for every real numbers x . Then,

Options

Ah is not continuous for all x
Bh is differentiable for all x
Ch^ (x) 1 , for all x 1
Dh is not differentiable at two values of x

Correct answer

D. h is not differentiable at two values of x

Step-by-step solution

h(x)= (x, x^2 )= array cl x, & x 0 x^2, & 0 x 1 x, & x 1 array . It is evident from the above graph that the given function is continuous for all x . Since, there are sharp edges at x=0 and x=1 , the function is not differentiable at these points. Also, at x 1 , the function represents a straight line having slope 1 , therefore h^ (x)=1, x 1 .

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