Identify the domain of f(x)= (x+3)/(x^2+3x+10)
x^2+3x+10 is the denominator. We want to ensure that the denominator cannot equal zero. Since x^2+3x+10 cannot equal zero, the domain for f(x) is all real numbers.
Find the derivative of f(x)=2x^2+3x-7
f'(x)= derivative of (2x^2)+ derivative of (3x) + derivative of (-7). The derivative can be broken up into individual parts. 1) derivative of (2x^2) is 4x (power rule) 2) derivative of (3x) is 3 (constant of a first degree) 3) derivative of (-7) is 0 (since its a constant)
Given: (x^2)+2x-7= 0, Solve for x.
Solution: x^2+2x-7=0 Restate Equation x^2+2x=7 Move "C" to the right x^2+2x+1=8 Create a perfect square by adding (b/2)^2 to both sides of the equation. (x+1)^2=8 Right the left side of the equation as a square. (x+1)= 8^(1/2) and -(x+1)=8^(1/2) Take the square root of both sides to get two simpler equations x=2(2)^(1/2)-1 x= -2(2)^(1/2)+1 Find the two solutions.