Question

Prove that the following functions do not have maxima or minima:

(i) f(x) = e^x (ii) g(x) = logx

(iii) h(x) = x³ + x² + x + 1

Answer 1

1. We have,

f(x) = e^x

Now, if. But, the exponential function can never assume 0 for any value of x.

Therefore, there does not exist c∈ R such that

Hence, function f does not have maxima or minima.

2. We have,

g(x) = log x

Therefore, there does not exist c∈ R such that.

Hence, function g does not have maxima or minima.

3. We have,

h(x) = x³ + x² + x + 1

Now,

h(x) = 0 ⇒ 3x² + 2x + 1 = 0 ⇒

Therefore, there does not exist c∈ R such that.

Hence, function h does not have maxima or minima.