Question

Given $h\left(x\right)=f\left(x\right)-g\left(x\right).If{h}^{\prime }\left(x\right)\ge 0,f\left(x\right)\ge g\left(x\right)$.

• A. True
• B. False

Answer 1

The correct option is B

False

If h’(x) $\ge$ 0, then we can say f’(x) - g’(x) $\ge$ 0

This would mean f’(x) $\ge$ g’(x)

We can’t say f(x) $\ge$ g(x) from this. For example, if f(x) = 1 and g(x) = 2, we get h(x) = 1-2 = -1

Now, h’(x) = 0. So the given conditions are satisfied.

But we can’t say f(x) $\ge$ g(x) from this.