Answer:
C. II and III
Step-by-step explanation:
See attachment for complete question
Given
[tex]f(x) = 4x + 6[/tex] differentiable at [tex]x = 3[/tex]
Start by representing y as [tex]f(x)[/tex];
[tex]f(x) = 4x + 6[/tex]
Solving (I): [tex]f(0) = 3[/tex]
Substitute 0 for x in [tex]f(x) = 4x + 6[/tex]
[tex]f(0) = 4 * 0 + 6[/tex]
[tex]f(0) = 0 + 6[/tex]
[tex]f(0) = 6[/tex]
I is not true
Solving (II): [tex]f(3) = 18[/tex]
Substitute 3 for x in [tex]f(x) = 4x + 6[/tex]
[tex]f(3) = 4 * 3 + 6[/tex]
[tex]f(3) = 12 + 6[/tex]
[tex]f(3) = 18[/tex]
II is true
Solving (III): [tex]f'(3) = 4[/tex]
First , we have to differentiate [tex]f(x)[/tex]
[tex]f(x) = 4x + 6[/tex]
[tex]f'(x) = 1 * 4x^{1 - 1} + 0[/tex]
[tex]f'(x) = 1 * 4x^{0} + 0[/tex]
[tex]f'(x) = 1 * 4 + 0[/tex]
[tex]f'(x) = 4[/tex]
Then, substitute 3 for x in [tex]f'(x) = 4[/tex]
[tex]f'(3) = 4[/tex]
III is true
