Chapter 3 - The Derivative In Graphing And Applications - Chapter 3 Review Exercises - Page 263: 72

$$f(x)=x^{3}-4x+5$$

$$f'(x)=g'(x)$$ $$\int f'(x) dx=\int g'(x) dx$$ $$f(x)=g(x)+c$$ $$f(x)=x^{3}-4x+6+c$$ Find $c$ using that $f(1)=2$. $$f(1)=1^{3}-4\cdot 1+6+c$$ $$2=1^{3}-4\cdot 1+6+c$$ $$2=1-4+6+c$$ $$2=3+c$$ $$2-3=c$$ $$-1=c$$ So the equation of $f$ is: $$f(x)=x^{3}-4x+6-1$$ $$f(x)=x^{3}-4x+5$$