Find Increasing and Decreasing interval of a definite integral

[flint gazelle]

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[clever spindle]

use the FFTC and take the derivative of the integral:
I=F(x)-F(4)
F(4) is a constant so will go to 0
F(x)→f(x)
now we want to figure out the interval for which t² is positive, which is (-∞,∞)

an alternative method is to simply integrate it:
⅓t³→ ⅓x³-(64/3)
take the derivative:
x²

[slow leaf]

doesnt zero on x^2 equals zero which is not increasing?

and zero is within (-inf, +inf)

[clever spindle]

strictly increasing excludes it and increasing includes it

[slow leaf]

how do i know when to treat a function as strictly increasing?

[clever spindle]

strictly increasing is when it has a derivative always above zero, or when the graph has no flat points

increasing is when the derivative is greater than or equal to zero, so the graph can have flat points but no turning points

but further on you might get to different definitions for strictly increasing

which would deem this function strictly increasing too

[slow leaf]

i see ty

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