Question

if f'(x) and g'(x) exist and f'(x) > g'(x) for all real x then the graph of f(x) and g(x) intersect or not

Answer 1

Step-by-step explanation:

Yes interesting because if we take f(x) =e^x and g(x) =1.

Answer 2

If f'(x) and g'(x) exist and f'(x) > g'(x) for all real x then the graph of f(x) and g(x) intersect no more that once.

• Let h(x) = f(x) - g(x) and we rephrase the question by asking about the number of roots of h(x) given that h'(x) > 0.
• By the Mean Value Theorem, two distinct roots would imply a point where h'(a) = 0. Therefore, there cannot be more than one intersection between f'(x) and g'(x).

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