Implicit differentiation
take the deritivive with respect to x
first
y+2=(1/2)(x^2)-2sin(y)
take deritivitive
dy/dx+0=1/2(2x)-2(cosy)dy/dx
dy/dx=x-2cosy(dy/dx)
add 2cosy(dy/dx) to both sides
dy/dx+2cosy(dy/dx) =x
undistribute dy/dx
dy/dx(1+2cos(y))=x
divide both sides by 1+2cos(y)
at (2,0)
x=2
y=0
the slope is 2/3
8am : -14F
noon : -14+10 = -4F
increase between noon and 4 is 2*10 =20
4 pm: -4F + 20 = 16F
temperature at 4 pm is 16F
I’m not sure so I’m gonna take an educated guess. I think it’s 1/3x
4 1/2 times 2 equals to 9.
it is the same as 4 1/2 plus 4 1/2 and 4 plus 4 is 8 and 1/2 plus 1/2 is 1 and 8 plus 1 is 9
answer is 9
Answer:
<span><span><span>f<span>−1</span></span><span>(x)</span></span>=<span><span>x−3</span>2</span></span>
Explanation:
Follow the steps:
<span><span>f<span>(x)</span></span>=2x+3</span>
1- replace <span><span>f<span>(x)</span></span> with y →y=2x+3</span>
2- simply switch <span>x and</span> so the equation looks like <span>x=2y+3</span>
3- use algebra to solve<span> for y</span>. (isolate y)
<span>x=2y+3</span>
<span>x−3=2y</span>
<span><span><span>x−3</span>2</span>=y</span>
This is the inverse function and is written as
<span><span><span>f<span>−1</span></span><span>(x)</span></span>=<span><span><span>x−3</span>2</span></span></span>