Basic maths-calculus-Q6

+1 vote

If f(x) is continuous & differentiable, f(1) = 10 and f'(x)\geq3 in 1\leq x\leq 4 then the smallest value of f(4) can be

(A) 10

(B) 13

(C) 14

(D) 19

asked May 19 in Basic Maths by gbeditor (44,560 points)
reshown May 24 by gbeditor

1 Answer

0 votes
 
Best answer

You can answer this using Lagrange Mean value theorem.

 

\\ f'(x)=\dfrac {f(b)-f(a)}{b-a}\\ \\ f'(x)=\dfrac{f(4)-f(1)}{4-1}\\ \\ f'(x)=\dfrac{f(4)-10}{3}\\ \\ 3=\dfrac{f(4)-10}{3}\\ \\ 9+10=f(4)\\ \\ 19=f(4)

answered May 27 by deepak-gatebook (112,760 points)
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