The tangent line to <em>y</em> = <em>f(x)</em> at a point (<em>a</em>, <em>f(a)</em> ) has slope d<em>y</em>/d<em>x</em> at <em>x</em> = <em>a</em>. So first compute the derivative:
<em>y</em> = <em>x</em>² - 9<em>x</em> → d<em>y</em>/d<em>x</em> = 2<em>x</em> - 9
When <em>x</em> = 4, the function takes on a value of
<em>y</em> = 4² - 9•4 = -20
and the derivative is
d<em>y</em>/d<em>x</em> (4) = 2•4 - 9 = -1
Then use the point-slope formula to get the equation of the tangent line:
<em>y</em> - (-20) = -1 (<em>x</em> - 4)
<em>y</em> + 20 = -<em>x</em> + 4
<em>y</em> = -<em>x</em> - 24
The normal line is perpendicular to the tangent, so its slope is -1/(-1) = 1. It passes through the same point, so its equation is
<em>y</em> - (-20) = 1 (<em>x</em> - 4)
<em>y</em> + 20 = <em>x</em> - 4
<em>y</em> = <em>x</em> - 24
Answer:
i tried but i dont understand sorry
Step-by-step explanation:
For this case you must simplify the expression respecting the rules of multiplication of mathematics.
The steps to simplify the expression are the following:
First multiply what is in the parentheses
-2x ^ 2 (x - 5) + x (2x ^ 2 - 10x) + x
-2x ^ 3 + 10x ^ 2 + 2x ^ 3 - 10x ^ 2 + x
Then add the terms that have the same exponent
(-2x ^ 3 + 2x ^ 3) + (10x ^ 2 - 10x ^ 2) + x
x
The final simplification is
x
answer
x
Answer:
it will be the last box to make a right triangle
Answer:
Step-by-step explanation:
