Search any question & find its solution
Question:
Answered & Verified by Expert
If $f^{\prime}(x)=k(\cos x-\sin x), f^{\prime}(0)=3, f\left(\frac{\pi}{2}\right)=15$, then $f(x)=$
Options:
Solution:
1492 Upvotes
Verified Answer
The correct answer is:
$3(\sin x+\cos x)+12$
$f^{\prime}(x)=k(\cos x-\sin x)$
$f^{\prime}(0)=3 \quad f(\pi / 2)=15$
$k=3$ then $f(x)=8$
Integrate $f^{\prime}(x)$
$f(x)=k \sin x+k \cos x+c$
$f(x)=3 \sin x+3 \cos x+c$
$f(\pi / 2)=15$
$c+3=15$
$c=12$
$f(x)=3 \sin x+3 \cos x+12$
$f^{\prime}(0)=3 \quad f(\pi / 2)=15$
$k=3$ then $f(x)=8$
Integrate $f^{\prime}(x)$
$f(x)=k \sin x+k \cos x+c$
$f(x)=3 \sin x+3 \cos x+c$
$f(\pi / 2)=15$
$c+3=15$
$c=12$
$f(x)=3 \sin x+3 \cos x+12$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.