yes, you are correct.

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Ashwin Kulkarni
asked
in Calculus
Jan 1, 2018

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3 votes

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But if we find pointwise

f(5)=25-30+666=661

f(4)=658

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Now again f(2)=658

f(1)=661

f(0)=666

f(-1)=673

So, cannot we tell , it is only increasing function?

Moreover, we get slope, where there is two values x and y

But we are here calculating only one value of x.

Where am I mistaking?

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$f(x) = x^2 - 6x + 666$

$f'(x) = 2x-6$

1) Find critical points, here $3$ is critical point.

2) find sign in the intervals $(-\infty,3),(3, \infty)$

3) take any values say x=1 in $(-\infty,3)$ then $f'(x)$ is -ve

function is decreasing

4) take any values say x=4 in $(3,\infty)$ then $f'(x)$ is +ve

function is increasing.

$f'(x) = 2x-6$

1) Find critical points, here $3$ is critical point.

2) find sign in the intervals $(-\infty,3),(3, \infty)$

3) take any values say x=1 in $(-\infty,3)$ then $f'(x)$ is -ve

function is decreasing

4) take any values say x=4 in $(3,\infty)$ then $f'(x)$ is +ve

function is increasing.

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