Answer to Question #151226 in Calculus for kitto

Question

statements is TRUE or FALSE

1 If y = eg(x) , then dy/dx = eg(x) / g(x) .

2. If for all x in (a, b), then f (x) is increasing on (a, b).

3. y = 6+2x-x2 has relative minimum at x=1, y=7.

4. ∫ xn dx= xn+1 / n+1 + C if n ≠ 1 .

Answer 1

1. FALSE

$\frac{d(e^{g(x)})}{dx}=g'(x) e^{g(x)}$

2. FALSE

Here is a counter-example. If $x \in (-5,0). f(x)=x^2$ is decreasing on $(-5,0)$

3. FALSE

y has relative maximum at x=1 and y=7

4. TRUE

$\int x^ndx=\frac{x^{n+1}}{n+1}+C, n\neq-1$