\( \operatorname { lx } _ { x \rightarrow 0 } = \sqrt { 1 + 3 x - 1 } \quad \lim \neq \frac { 0 } { 0 } \)

Find the intervals on which \( f \) is increasing and the intervals on which it is decreasing. \( f(x)=\frac{x^{4}}{4}-3 x^{3}+9 x^{2} \)

Find an equation of the line tangent to the given curve at \( \mathrm{x}=\mathrm{a} \). \[ y=4+6 x+11 x e^{x} ; a=0 \] The equation for the tangent line is \( y=\square \).

Suppose that \( f(x, y)=x^{4}+y^{4}-x y \). Then the minimum value of \( f(x, y) \) is.. A. -0.125 B. 0.125 C. 0 D. None of these answers

Determine the intervals on which the following function is concave up or concave down. Identify any inflection points. \( f(x)=x^{4}-3 x^{3}+9 \)

Find the derivative of the following function. \( g(t)=4 \sqrt{t} \) \( g^{\prime}(t)=\square \)