- #1
myanmar
- 33
- 0
1. Find [tex]\frac{dy}{dx}[/tex] and [tex]\frac{d^{2}y}{dx^{2}}[/tex] if [tex]\int^{3x}_{1} \frac{1}{t^{2}+t+1}\,dt[/tex]
I expect that I'd make [tex]u=3x[/tex], then [tex]du=3dx[/tex]. I think when I differentiate, I'd end up with [tex]\frac{dy}{dx}=\frac{1}{3t^{2}+3t+3}[/tex]. I think that [tex]\frac{d^{2}y}{dx^{2}}[/tex] would just be the derivative of [tex]\frac{dy}{dx}[/tex]
2. Find and classify the relative maxima and minima of [tex]f(x)[/tex], if
f(x) = [tex]\int^x_0 \frac{t^{2}-{4}}{{1}+{cos}^{2}{t}}\,dt[/tex]
I think to find max and min, I just need to find the second derivative and solve for zero right? Is the first derivative [tex]\frac{x^{2}-{4}}{{1}+{cos}^{2}{x}}[/tex]?
I expect that I'd make [tex]u=3x[/tex], then [tex]du=3dx[/tex]. I think when I differentiate, I'd end up with [tex]\frac{dy}{dx}=\frac{1}{3t^{2}+3t+3}[/tex]. I think that [tex]\frac{d^{2}y}{dx^{2}}[/tex] would just be the derivative of [tex]\frac{dy}{dx}[/tex]
2. Find and classify the relative maxima and minima of [tex]f(x)[/tex], if
f(x) = [tex]\int^x_0 \frac{t^{2}-{4}}{{1}+{cos}^{2}{t}}\,dt[/tex]
I think to find max and min, I just need to find the second derivative and solve for zero right? Is the first derivative [tex]\frac{x^{2}-{4}}{{1}+{cos}^{2}{x}}[/tex]?
Last edited: