Tutor profile: Taylor D.
Solve the Inequality: (-(x/4) + 3) > 8
Things to know when solving inequalities: - what you do to one side, you do to both - multiplying/dividing both sides of the inequality by a negative will cause the sign to flip To solve this inequality we want to start by subtracting 3 on both sides to get x all by itself. So, (-(x/4) + 3 -3) > 8-3 -(x/4) > 5 Now we multiply both sides by 4 -x > 20 Since we are looking for x, not -x, we multiply both sides by (-1). Rember that multiplying by a negative will flip the inequality sign. So, x<-20
Find the first derivative of: f(x)= 8(x^3) + 2(x^2) + x + 4
The Rule of Solving Derivatives: example: f(x)= b(N^a) To find the derivative, multiple the coefficient, b, by the exponent, a. Then our variable, N, is now raised the original power minus 1. So, we have f'(x)= (b*a)(N^(a-1)) When there is no variable, just a coefficient, the exponent is thought of as zero. Thus when the exponent, 0, is multiplied by the coefficient. We have 0. Now we can apply this thinking to our problem: f(x)= 8(x^3) + 2(x^2) + x + 4 f'(x)= (8*3)(x^(3-1)) + (2*2)(x^(2-1)) + (1*1)(x^(1-1)) + (4*0)(x^(0-1)) f'(x)= 24(x^2) + 4x + 1
We will use the FOIL method to complete this problem. 1. Multiply the terms in parenthesis in this order F- first terms ((6x^3) * (x^2)) =6(x^5) O- outside terms ((6x^3) * (-6)) =-36(x^3) I- inside terms (4 * (x^2)) =4(x^2) L- last terms (4 * -6) =-24 Thus, we combine like terms if necessary and write our finding in one equation: 6(x^5) - 36(x^3) + 4(x^2) - 24
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