If f(3)=11,f(3)=11, f′f′ is continuous, and ∫73f′(t)dt=20,∫37f′(t)dt=20, what is the value of f(7)?

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09-12-2017
Mathematics

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If f(3)=11,f(3)=11, f′f′ is continuous, and ∫73f′(t)dt=20,∫37f′(t)dt=20, what is the value of f(7)?

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LammettHash LammettHash · Answer 1 · 2017-12-09T19:10:36+01:00

LammettHash LammettHash

09-12-2017

Since [tex]f'[/tex] is continuous, we have by the fundamental theorem of calculus

[tex]\displaystyle\int_3^7f'(t)\,\mathrm dt=f(7)-f(3)=20[/tex]

We're given that [tex]f(3)=11[/tex], so it follows that [tex]f(7)=31[/tex].

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