Question

Consider the function and the value of a.

f(x) = 5 - x - x^2, a = 0
(a) Use Mtan = lim h->0 [f(a + h) – f(a)] / h
to find the slope of the tangent line mtan = f'(a).​

Answer 1

Mtan=1-2a

Explanation:

Mtan=lim h->0[5-(a+h)-(a+h)^2-(5-a-a^2)/h

=lim h->0[5-a-h-a^2-2ah-h^2-5+a+a^2]/h

=lim h->0[h-2ah-h^2+5-5-a+a-a^2+a^2]/h

=lim h->[h-2ah-h^2 +0+0+0]/h

=lim h->o[h(1-2a-h)/h

=lim h->0 (1-2a-h)

=1-2a-0

=1-2a

Mtan=1-2a.