Find pt on 3 cos(x) where inst. rate of change is -1.5

[babaoriley1981]

There is a point on the graph of f(x) = 3cosx (shown above) at which the instantaneous rate of change of f(x) is -1.5. Find the coordinates of that point.

can anyone help?

 

[soroban]

Re: really need help asap with calculus problem!

Hello, babaoriley1981!

There is a point on the graph of $\displaystyle f(x)\:=\:3\cdot\cos x$ (shown above)
at which the instantaneous rate of change of $\displaystyle f(x)$ is $\displaystyle \,-1.5$
Find the coordinates of that point.

The instantaneous rate of change is given by the derivative: $\displaystyle \:f'(x)\:=\:-3\cdot\sin x$

So we have: $\displaystyle \;-3\cdot\sin x\:=\:-1.5\;\;\Rightarrow\;\;\sin x\:=\:0.5\;\;\Rightarrow\;\;x\:=\:\frac{\pi}{6},\:\frac{5\pi}{6},\:\cdots$

Since I can't see the graph from here,
. . you decide which value is appropriate.