Answer:
[tex]c=\frac{1}{16}[/tex]
Step-by-step explanation:
[tex]f(x)=\sqrt{2x}[/tex]
[tex]f'(x)=\frac{\sqrt{2x}}{2x}[/tex]
[tex]f'(1)=\frac{\sqrt{2}}{2}[/tex]
[tex]f'(c)=\frac{\sqrt{2c}}{2c}[/tex]
[tex]f'(c)=4f'(1)[/tex]
[tex]\frac{\sqrt{2c}}{2c}=4(\frac{\sqrt{2}}{2})[/tex]
[tex]\frac{\sqrt{2c}}{2c}=2\sqrt{2}[/tex]
[tex]\sqrt{2c}=4c\sqrt{2}[/tex]
[tex]2c=32c^2[/tex]
[tex]2=32c[/tex]
[tex]\frac{1}{16}=c[/tex]
