Question

Find the equation of the line tangent to f(x)=-2sin(x) at x=34?.

Answer 1

The equation for the tangetnt line is,

y = -1.66x + 55.32

Explanation:

WE ASSUME THAT THE FUNCTION IS IN DEGREES!!!

We have f(x) = -2sin(x)

Taking the derivative, we get,

f'(x) = -2cos(x)

Now, this is the slope for any point x, so

at x = 34, we get,

m = f'(34) = -2cos(34)

m = -1.66

And at this point, the value of the function is,

f(34) = -2sin(34)

f(34) = -1.12

Then, using the point-slope form, we get,

y - f(34) = m(x - 34)

y + 1.12 = -1.66(x - 34)

y = -1.66x + 56.44 - 1.12

y = -1.66x + 55.32