If f(4) = 9 and f ′(x) ≥ 2 for 4 ≤ x ≤ 9, how small can f(9) possibly be?f(9) ≥
Question
If f(4) = 9 and f ′(x) ≥ 2 for 4 ≤ x ≤ 9, how small can f(9) possibly be?
f(9) ≥
Solution
Given that f(4) = 9 and f ′(x) ≥ 2 for 4 ≤ x ≤ 9, we can use the Mean Value Theorem which states that there exists some c in the interval [4,9] such that f'(c) = (f(9)-f(4))/(9-4).
We know that f'(x) ≥ 2, so we can set f'(c) to its minimum value of 2.
So, 2 = (f(9)-9)/5 Solving for f(9), we get f(9) = 2*5 + 9 = 19.
Therefore, the smallest possible value for f(9) is 19.
Similar Questions
If f(x) is continuous & differentiable,f(1) = 10 and f’(x) ≥ 3 in 1 ≤ x ≤ 4 thenthe smallest value of f(4) can beA. 10 B. 13C. 14 D. 19
Suppose that 4 ≤ f ′(x) ≤ 5 for all values of x. What are the minimum and maximum possible values of f(6) − f(3)? ≤ f(6) − f(3)
A function f(x) increases by a factor of 1.9 over every unit interval in x and f(0)=2.Which could be a function rule for f(x)?
If f(4) = 11, f ' is continuous, and 6f '(x) dx4 = 18, what is the value of f(6)?f(6) =
he function A is defined for x ≥ 2 by A(x) =∫ x2(t2 − 9)3 dt. [5 marks]Determine A(2) and A′(3)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.