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Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: $(iii)\: f (x) =4x-\large\frac{x^2}{2}$$, x \in [– 2, \large\frac{9}{2}] $

This is third part of multipart q5

1 Answer

  • $\large\frac{d}{dx}(x^n)$$=nx^{n-1}$
Step 1:
On differentiating with respect to x we get
For extreme values $f'(x)=0$
Step 2:
Now we find the values of $f(x)$ at $x=-2,4,\large\frac{9}{2}$
Step 3:
Step 4:
$f(\large\frac{9}{2})=$$4\times \large\frac{9}{2}-\large\frac{1}{2}$$\times \large \frac{81}{4}$
Step 5:
At $x=4$,absolute maximum value$=8$
At $x=2$, absolute minimum value $=-10$
answered Aug 7, 2013 by sreemathi.v
edited Aug 30, 2013 by sharmaaparna1

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