Distribute the 15 through the parentheses, like so-
30b+45
Y=-3x+1
1 raises the y intercept and -3 is the slope that we can see from (0,1) to (1,-2)
Calculus 1?
To find concavity you must take the second derivative.
As you would to find your local maximums and minimums (critical points) in the first derivative by setting y' = 0, to find points of inflection you set acceleration, y" = 0.
Now that you know where the point in which the function is neither concave up or concave down (at the points of inflection) plug x-values between them into the second derivative for x. If y" is positive between those particular points will be concave up and if y" is negative it will be concave down between that interval.
For a better understanding you might find a good video on Youtube explaining this if you search "Points of Inflections" or "Concavity of a function".
Cheers.
2l + 2w = 100
l + w = 50 . . . (1)
w = 2l - 4 . . . (2)
l + 2l - 4 = 50
3l - 4 = 50
3l = 50 + 4 = 54
l = 54/3 = 18
w = 2(18) - 4 = 36 - 4 = 32
Therefore, the width of the picture frame is 32 cm.
(3) Differentiating both sides of
with respect to <em>x</em> gives
Solve for d<em>y</em>/d<em>x</em> :
Then the slope of the tangent line to the curve at (1, 9) is
The equation of the tangent line would then be
<em>y</em> - 9 = -2/3 (<em>x</em> - 1) ==> <em>y</em> = -2/3 <em>x</em> + 29/3
(4) The slope of the tangent line to
at a point <em>(x, y)</em> on the curve is
When <em>x</em> = -1, we have a slope of 2/3, so
-(2<em>a</em> + 1)/(-1 - 2)² = 2/3
Solve for <em>a</em> :
-(2<em>a</em> + 1)/9 = 2/3
2<em>a</em> + 1 = -18/3 = -6
2<em>a</em> = -7
<em>a</em> = -7/2
