identify any maximum or minimum values on the interval $-2leq xleq3$.\n15. $f(x)=5x - 2$\n16. $f(x)=-2x - 4$
identify any maximum or minimum values on the interval $-2leq xleq3$.\n15. $f(x)=5x - 2$\n16. $f(x)=-2x - 4$
Answer
Explanation:
Step1: Analyze the function (f(x)=5x - 2)
The function (y = 5x-2) is a linear function with slope (m = 5>0). A linear function with positive slope is increasing. On the interval (-2\leq x\leq3): When (x=-2), (f(-2)=5\times(-2)-2=-10 - 2=-12) When (x = 3), (f(3)=5\times3-2=15 - 2 = 13)
Step2: Analyze the function (f(x)=-2x - 4)
The function (y=-2x - 4) is a linear function with slope (m=-2<0). A linear function with negative slope is decreasing. On the interval (-2\leq x\leq3): When (x=-2), (f(-2)=-2\times(-2)-4=4 - 4=0) When (x = 3), (f(3)=-2\times3-4=-6 - 4=-10)
Answer:
For (f(x)=5x - 2): Minimum value is (-12) (at (x = - 2)) and maximum value is (13) (at (x = 3)). For (f(x)=-2x - 4): Maximum value is (0) (at (x=-2)) and minimum value is (-10) (at (x = 3)).