Sketch the graph of f by hand and use your sketch to find the absolute maximum and minimum values of f. (If an answer does not exist, enter DNE.)f(x) = 1 − x if 0 ≤ x < 44x − 16 if 4 ≤ x ≤ 8absolute maximum absolute minimum
Question
Sketch the graph of f by hand and use your sketch to find the absolute maximum and minimum values of f. (If an answer does not exist, enter DNE.)f(x) = 1 − x if 0 ≤ x < 44x − 16 if 4 ≤ x ≤ 8absolute maximum absolute minimum
Solution
To sketch the graph of the function f(x), we first need to understand that it is a piecewise function with two parts: f(x) = 1 - x for 0 ≤ x < 4 and f(x) = 4x - 16 for 4 ≤ x ≤ 8.
Step 1: Sketch the first part of the function f(x) = 1 - x for 0 ≤ x < 4. This is a straight line with a negative slope starting from the point (0,1) and ending at the point (4,-3).
Step 2: Sketch the second part of the function f(x) = 4x - 16 for 4 ≤ x ≤ 8. This is also a straight line but with a positive slope starting from the point (4,-16) and ending at the point (8,16).
Step 3: Combine the two parts to get the complete graph of the function f(x).
Step 4: From the graph, we can see that the absolute maximum value of f(x) is 1, which occurs at x = 0. The absolute minimum value of f(x) is -16, which occurs at x = 4.
Similar Questions
Sketch the graph of f by hand and use your sketch to find the absolute maximum and minimum values of f. (If an answer does not exist, enter DNE.)f(x) = 16 − x2 if −4 ≤ x < 03x − 3 if 0 ≤ x ≤ 4absolute maximum absolute minimum
Find the absolute maximum and absolute minimum values of f on the given interval.f(x) = 6x4 − 8x3 − 24x2 + 1, [−2, 3]absolute minimum value absolute maximum value
Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values of f. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = sin(x), −𝜋 2 ≤ x ≤ 𝜋 2 absolute maximum value absolute minimum value local maximum value(s) local minimum value(s)
Find the absolute maximum and absolute minimum values of f on the given interval.f(x) = 3 + 81x − 3x3, [0, 4]absolute minimum value absolute maximum value
Find all relative extrema of the function. Use the second derivative test where applicable. (If an answer does not exist, enter DNE.)f(x) = x4 − 8x3 + 1
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.