Minimum & Maximum

[jennymatt42]

I have no idea how to do this problem, someone please help!

Within the interval ( -1.57, 2.91 ), for what value of x does f(x) take on a minimum if
f(x) = 6.4 sin(1.4 x) ?8.7 cos(1.4 x)

Within the interval ( -1.57, 2.91 ), for what value of x does f(x) take on a maximum if
f(x) = 6.4 sin(1.4 x) ?8.7 cos(1.4 x)

please help meee!!

 

[galactus]

I have no idea how to do this problem, someone please help!

Within the interval ( -1.57, 2.91 ), for what value of x does f(x) take on a minimum if
f(x) = 6.4 sin(1.4 x) ?8.7 cos(1.4 x)

Within the interval ( -1.57, 2.91 ), for what value of x does f(x) take on a maximum if
f(x) = 6.4 sin(1.4 x) ?8.7 cos(1.4 x)

please help meee!!

I am going to write this out in fractions.

\(\displaystyle f(x)=\frac{32}{5}sin(\frac{7x}{5})-\frac{87}{10}cos(\frac{7x}{5})\)

Find the derivative, set to 0 and solve for x.

\(\displaystyle f'(x)=\frac{224}{25}cos(\frac{7x}{5})+\frac{609}{50}sin(\frac{7x}{5})\)

\(\displaystyle \frac{224}{25}cos(\frac{7x}{5})=-\frac{609}{50}sin(\frac{7x}{5})\)

Can you solve for x?. Remember that \(\displaystyle \frac{sin(x)}{cos(x)}=tan(x)\)

When you solve for x, add on the period of the function. It is \(\displaystyle \frac{5C{\pi}}{7}\). Where C takes on integer values both negative and positive. Let C=0, 1, 2, ..... and see which values fall in the given interval. These values of C will give the max and min's as seen on the graph.