slope: 22
instantaneous: 22 1/2
f(x)=2x^4+5x^3-x^2-3x+1
a)Determine the average slope between the points where x=1 and x=3.
b)Determine the instantaneous slope at each of these points.
2 answers
f(1) = 2 + 5 - 1 - 3 + 1 = 4
f(3) = 162 + 135 - 9 - 9 + 1 = 280
for between the points (1,4) and (3,280)
slope = (280-4)/(3-1) = 138
f'(x) = 8x^3 + 15x^2 - 2x - 3
f ' (1) = 8+15 - 2 - 3 = 18
at (1,4) the real slope is 18
f ' (3) = 216 + 135 - 6 - 3 = 342
at (3,280) the slope is 342
f(3) = 162 + 135 - 9 - 9 + 1 = 280
for between the points (1,4) and (3,280)
slope = (280-4)/(3-1) = 138
f'(x) = 8x^3 + 15x^2 - 2x - 3
f ' (1) = 8+15 - 2 - 3 = 18
at (1,4) the real slope is 18
f ' (3) = 216 + 135 - 6 - 3 = 342
at (3,280) the slope is 342