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melamori03 [73]

2 years ago

5

Find f '(−5), if f(x) = (−4x2 − 2x)(−x2 − 9)

1 answer:

Y_Kistochka [10]2 years ago

7 0

<span>*Answer*
x+0 or x=-0.63297

</span><span><span>heres step by step
−<span>5x</span></span>=<span><span>(<span><span>−<span>4<span>x2</span></span></span>−<span>2x</span></span>)</span><span>(<span><span>−<span>x2</span></span>−9</span>)</span></span></span><span><span>−<span>5x</span></span>=<span><span><span><span>4<span>x4</span></span>+<span>2<span>x3</span></span></span>+<span>36<span>x2</span></span></span>+<span>18x
</span></span></span>heres step by step

Step 1: Subtract 4x^4+2x^3+36x^2+18x from both sides

<span><span><span>−<span>5x</span></span>−<span>(<span><span><span><span>4<span>x4</span></span>+<span>2<span>x3</span></span></span>+<span>36<span>x2</span></span></span>+<span>18x</span></span>)</span></span>=<span><span><span><span><span>4<span>x4</span></span>+<span>2<span>x3</span></span></span>+<span>36<span>x2</span></span></span>+<span>18x</span></span>−<span>(<span><span><span><span>4<span>x4</span></span>+<span>2<span>x3</span></span></span>+<span>36<span>x2</span></span></span>+<span>18x</span></span>)</span></span></span><span><span><span><span><span>−<span>4<span>x4</span></span></span>−<span>2<span>x3</span></span></span>−<span>36<span>x2</span></span></span>−<span>23x</span></span>=0

</span>Step 2: Factor left side of equation

<span><span>x<span>(<span><span><span><span>−<span>4<span>x3</span></span></span>−<span>2<span>x2</span></span></span>−<span>36x</span></span>−23</span>)</span></span>=0</span>Step 3: Set factors equal to 0.<span><span>x=<span><span><span><span><span>0<span> or </span></span>−<span>4<span>x3</span></span></span>−<span>2<span>x2</span></span></span>−<span>36x</span></span>−23</span></span>=0</span><span><span>x=<span><span>0<span> or </span></span>x</span></span>=<span>−0.63297</span></span>

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