i suppose these are calculus questions...

for image003 the function ..

a)

at x=1, , hence the equation of the tangent line at the point (1,6) is y-6 = 8(x-1) and the equation of the line perpendicular to it is

b) solve for and plug in the values of x in f(x) to find their corresponding ordinates..

c) on the interval [-1,2]

f(-1) = -2

f(2) = 19

and f(-1)f(2) = -38 < 0

so, by a corollary to the IVT, there is a c such that f(c) = 0.

indeed, , solving for c, we have (using a calculating device) -.8519, and 4.0453

Ü