Correct Answer - Option 4 : Function does not have local maxima or minima.
Concept:
Following steps to finding maxima and minima using derivatives.
- Find the derivative of the function.
- Set the derivative equal to 0 and solve. This gives the values of the maximum and minimum points.
- Now we have find second derivative.
- f``(x) is less than 0 then the given function is said to be maxima
- If f``(x) Is greater than 0 then the function is said to be minima
Calculation:
Given:
f(x) = ex
Differentiating with respect to x, we get
⇒ f’(x) = ex
For maximum value f’(x) = 0
∴ f’(x) = ex = 0
Exponential function can never assume zero for any value of x, therefore function does not have local maxima or minima.