For fx x 5 find fa h fah if h does not equal 0Solutionfx

For f(x) = -x² + 5, find (f(a + h) - f(a)/h) if h does not equal 0?

Solution

f(x) = -x² + 5

f(a) = -a² + 5

f(a+h) = -(a+h)² + 5 = -(a² +2ah + h²) + 5

==> f(a+h) = -a² -2ah - h² + 5

[f(a + h) - f(a)]/h = [-a² -2ah - h² + 5 - (-a² + 5)]/h

==> [-a² -2ah - h² + 5 + a² - 5]/h

==> [-2ah - h²]/h

==> [h(-2a - h)]/h

==> -2a-h

Hence [f(a + h) - f(a)]/h = -2a-h