Find two positive numbers that satisfy the given requirements.The product is 147 and the sum of the first number plus three times the second number is a minimum.

Find the linear approximation of the function $f(x)=\sqrt{1-x}$ at $a=0$ and use it to approximate the numbers $\sqrt{0.9}$ and $\sqrt{0.99}$.

Determine whether each of these functions is a bijection from R to R.

a) $f(x)=-3x+4$

b) ${\displaystyle f\left(x\right)=-3x^2+7}$

c) $f(x)=\frac{x+1}{x+2}$
${\displaystyle d)f\left(x\right)=x^5+1}$

A baseball team plays in a stadium that holds 55,000 spectators. With ticket prices at 10, the average attendance had been 27,000. When ticket prices were lowered to10,the average attend ance had been 27,000.When ticket prices were lowered to 8, the average attendance rose to 33,000. How should ticket prices be set to maximize revenue?

Form a polynomial f(x) with real coefficients the given degree and zeros. Degree 4, Zeros:, 4-4i, -5 multiplicity 2

Classify each function:
a) ${\displaystyle f\left(x\right)=\log 3\left(x\right)}$
b) ${\displaystyle g\left(x\right)=\sqrt[5]{x}}$
c) ${\displaystyle h\left(x\right)=2\frac{x^3}{8–x^2}}$
d) ${\displaystyle u\left(t\right)=1–1.1t_{2.51}{t}^2}$
e) ${\displaystyle v\left(t\right)=3^t}$
f) $w(\theta )=\sin \theta {\cos }^6\theta$

Find the exact length of the curve.
${\displaystyle y=\frac{x_3}{3}+\frac{1}{4}x,1\le x\le 2}$

If ${\displaystyle f\left(x\right)=e^x}$ and $g(x)=\log x$ show that $fog=gof$ given $x>0$