The twice–differentiable function f is defined for all real numbers and satisfies the following conditions: f(0)=3 f′(0)=5 f″(0)=7 the function g is given by g(x)=eax+f(x) for all real numbers, where a is a constant. find g ′(0) and g ″(0) in terms of a. show the work that leads to your answers. the function h is given by h(x)=cos(kx)[f(x)]+sin(x) for all real numbers, where k is a constant. find h ′(x) and write an equation for the line tangent to the graph of h at x=0. for the curve given by 4x2+y2=48+2xy show that dy dx = y−4x y−x . for the curve given by 4x2+y2=48+2xy, find the positive y-coordinate given that the x-coordinate is 2. for the curve given by 4x2+y2=48+2xy, show that there is a point p with x-coordinate 2 at which the line tangent to the curve at p is horizontal.

Given that and , it follows that

###

When , we have

The slope of the line tangent to at (0, 3) has slope ,

Then the tangent line at this point has equation

###

Differentiating both sides of

with respect to yields

On this curve, when we have

(ignoring the negative solution because we don't care about it)

The tangent to this curve at the point has slope . This tangent line is horizontal when its slope is 0. This happens for

and when , there is a horizontal tangent line to the curve at the point (2, 8).

b.my answer is b.

brainliest

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3