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Find the second derivative of y=x³−x²+2x+5

Mathematics

ScanSolve AI Answer

Graph of y = x³ − x² + 2x + 5

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Key points of y = x³ − x² + 2x + 5
Pointxy
x-intercept−1.130
y-intercept05

Step-by-step solution

2 steps

Here are the calculations based on the provided image. The function being evaluated is y=2x+5y = 2x + 5.

  1. Complete the table of values for y=2x+5y = 2x + 5.

    We substitute each xx value into the function to find the corresponding yy value.

    For x=14x=14:

    y=2(14)+5=28+5=33y = 2(14) + 5 = 28 + 5 = 33

    For x=7x=7:

    y=2(7)+5=14+5=19y = 2(7) + 5 = 14 + 5 = 19

    For x=3x=3:

    y=2(3)+5=6+5=11y = 2(3) + 5 = 6 + 5 = 11

    For x=1x=1:

    y=2(1)+5=2+5=7y = 2(1) + 5 = 2 + 5 = 7

    For x=2x=2:

    y=2(2)+5=4+5=9y = 2(2) + 5 = 4 + 5 = 9

    For x=4x=4:

    y=2(4)+5=8+5=13y = 2(4) + 5 = 8 + 5 = 13

    The completed table is:

    XY
    1433
    719
    311
    17
    29
    413
  2. Evaluate the function for specific xx values shown in the individual calculations.

    For x=3x=3:

    y=2(3)+5y = 2(3) + 5 y=6+5y = 6 + 5 y=11y = \boxed{\textbf{11}}

    For x=7x=7:

    y=2(7)+5y = 2(7) + 5 y=14+5y = 14 + 5 y=19y = \boxed{\textbf{19}}

    For x=1x=1:

    y=2(1)+5y = 2(1) + 5 y=2+5y = 2 + 5 y=7y = \boxed{\textbf{7}}

    For x=4x=4:

    y=2(4)+5y = 2(4) + 5 y=8+5y = 8 + 5 y=13y = \boxed{\textbf{13}}

    For x=0x=0:

    y=2(0)+5y = 2(0) + 5 y=0+5y = 0 + 5 y=5y = \boxed{\textbf{5}}

    For x=2x=2:

    y=2(2)+5y = 2(2) + 5 y=4+5y = 4 + 5 y=9y = \boxed{\textbf{9}}
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