Question

Find the slope of the tangent line to the graph of the function at the given point.

g(x) = 18 − x2; (2, 14)
Apply the Definition of Tangent Line with slope m,m = lim Δx →
f(c + Δx) − f(c)
Δx
,to the given function f(x) =
g(x) = 18 − x2
and c = 2.
At
x = 2, g(2) = ,
the coordinates of
(x, g(x))
are
(2, ).
step by step

Answer 1

Explanation:

use power rule of differentiation :

f(x) = xⁿ → f'(x) = nxⁿ-¹

g(x) = -x² + 18

g'(x) = -2x

m = g'(x)

m = g'(2)

m = -4

y - y1 = m(x - x1)

y - 14 = -4(x - 2)

y - 14 = -4x + 8

y + 4x = 22

y = -4x + 22

slope of the tangent line : -4

Subject : Mathematics

Level : SHS

Chapter : Differentiation