<span>3^4 ⋅ 3^−9
= 3^(4-9)
= 3^-5
= 1 / 3^5
= 1/243</span>
28.7083333333...
But you could also round it up to 29.
Compute the derivative of <em>y</em> = (<em>x</em>² + <em>x</em> - 2)² using the chain rule:
d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) d/d<em>x</em> [<em>x</em>² + <em>x</em> - 2]
d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) (2<em>x</em> + 1)
Evaluate the derivative at <em>x</em> = -1 :
d<em>y</em>/d<em>x</em> (-1) = 2 ((-1)² + (-1) - 2) (2 (-1) + 1) = 4
This is the slope of the tangent line to the function at (-1, 4).
Use the point-slope formula to get the equation for the tangent line:
<em>y</em> - 4 = 4 (<em>x</em> - (-1)) → <em>y</em> = 4<em>x</em> + 8
Real and rational and integer?
A = 1.5
B = -1/3
C = -4/3
A is a positive so there is only one possibility
B is in between 0 and -1, so it has to be -1/3
C is below -1 and so its the improper fraction