![\bf f(x)=x+\cfrac{1}{x}\qquad \left[\frac{1}{2},2 \right]\\\\ -----------------------------\\\\ \cfrac{df}{dx}=1+\left(-1x^{-2} \right)\implies \cfrac{df}{dx}=1-\cfrac{1}{x^2} \\\\\\ f'(c)=1-\cfrac{1}{c^2}\quad \quad 1-\cfrac{1}{c^2}=\cfrac{f(2)-f\left( \frac{1}{2} \right)}{2-\frac{1}{2}} \\\\\\ 1-\cfrac{1}{c^2}=\cfrac{\frac{5}{2}-\frac{5}{2}}{\frac{3}{2}}\implies 1-\cfrac{1}{c^2}=\cfrac{0}{\frac{3}{2}}\implies 1-\cfrac{1}{c^2}=0 \\\\\\ 1=\cfrac{1}{c^2}\implies c^2=1\implies c=\pm\sqrt{1}\implies c=\pm 1](https://tex.z-dn.net/?f=%5Cbf%20f%28x%29%3Dx%2B%5Ccfrac%7B1%7D%7Bx%7D%5Cqquad%20%5Cleft%5B%5Cfrac%7B1%7D%7B2%7D%2C2%20%20%5Cright%5D%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%5Ccfrac%7Bdf%7D%7Bdx%7D%3D1%2B%5Cleft%28-1x%5E%7B-2%7D%20%20%5Cright%29%5Cimplies%20%5Ccfrac%7Bdf%7D%7Bdx%7D%3D1-%5Ccfrac%7B1%7D%7Bx%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Af%27%28c%29%3D1-%5Ccfrac%7B1%7D%7Bc%5E2%7D%5Cquad%20%5Cquad%201-%5Ccfrac%7B1%7D%7Bc%5E2%7D%3D%5Ccfrac%7Bf%282%29-f%5Cleft%28%20%5Cfrac%7B1%7D%7B2%7D%20%5Cright%29%7D%7B2-%5Cfrac%7B1%7D%7B2%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A1-%5Ccfrac%7B1%7D%7Bc%5E2%7D%3D%5Ccfrac%7B%5Cfrac%7B5%7D%7B2%7D-%5Cfrac%7B5%7D%7B2%7D%7D%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Cimplies%201-%5Ccfrac%7B1%7D%7Bc%5E2%7D%3D%5Ccfrac%7B0%7D%7B%5Cfrac%7B3%7D%7B2%7D%7D%5Cimplies%201-%5Ccfrac%7B1%7D%7Bc%5E2%7D%3D0%0A%5C%5C%5C%5C%5C%5C%0A1%3D%5Ccfrac%7B1%7D%7Bc%5E2%7D%5Cimplies%20c%5E2%3D1%5Cimplies%20c%3D%5Cpm%5Csqrt%7B1%7D%5Cimplies%20c%3D%5Cpm%201)
there's a quick graph below of the bounds and the tangent at "c"
not happening -2 or 2 will have a tangent parallel to a,b, needless to say -2 is out of the range [a,b] anyway, so the only value is really 1, on the positive 1st quadrant
Answer:
x = 17
Step-by-step explanation:
<u>Area of a parallelogram:</u>
A = bh
<u>Given:</u>
A = 153
b = 9
<u>Work:</u>
A = bh
h = A/b
h = 153/9
h = 17
Answer:
y = 5x - 28
Step-by-step explanation:
y - y1 = m(x - x1)
y - 7 = 5(x - 7)
y - 7 = 5x - 35
add 7 to both sides to get rid of - 7 --> y = 5x -35 + 7
Answer:37.5 square inches
Step-by-step explanation:
We know that the number of cakes is dependent on the time spent in baking.
We are given that Carmen can bake 84 cakes in 1.6 hours, therefore, to know the number of cakes that she can bake in 2 hours, all you have to do is cross multiplication as follows:
number of cakes = (2*84) / 1.6 = 105 cakes