# Given range and first derivative values, find maximum pt

#### Wecoxepa

range [0,4]

0 <= f'(x) <=3

what is the maximum point?

so, I assume x=3 when f'(x)=4 (assuming some sort of f(x) curving upwards with the tangent slopes increasing from 0). Not sure how to get y from there.

maybe tanget line...y=mx+b...y=(4)(3)+b...y=12+b

but then what is the y-intercept, b? two unknowns.

been struggling with this without a function. Thank you for any help.

#### skeeter

Math Team

range [0,4]

0 <= f'(x) <=3

what is the maximum point?

so, I assume x=3 when f'(x)=4 ...
how can $f'(x)=4$ if the derivative values are $0 \le f'(x) \le 3$ ?

If the range of a function is $[0,4]$, then the maximum value of the function is $y=4$ ... also, the given interval of values for $f'$ indicates that $f(x)$ never decreases throughout its domain.

#### mathman

Forum Staff

range [0,4]

0 <= f'(x) <=3

what is the maximum point?

so, I assume x=3 when f'(x)=4 (assuming some sort of f(x) curving upwards with the tangent slopes increasing from 0). Not sure how to get y from there.

maybe tanget line...y=mx+b...y=(4)(3)+b...y=12+b

but then what is the y-intercept, b? two unknowns.

been struggling with this without a function. Thank you for any help.
Careful with terminology. Range means y values, domain means x values. I'll assume you meant domain [0,4]. Then the maximum is at f(4), but with no further information, that is all you can say.

If you really meant range [0,4], then 4 is the maximum value.