Find the equation of the normal to the curve which is parallel to the line

answer:

explanation

in order to find the equation of the normal to the given curve, we need the slope of the normal and the point on the curve.

the given line has a slope of 1/2. if this normal is parallel to this line, then the normal to the curve has a slope of 1/2 as well.

to find the point at which this normal is formed, we can use the location of the tangent. since the normal is perpendicular to tangent, the tangent line slope is the negative reciprocal: -2. we have to find the point at which the curve has a tangent with a slope of -2.

to find tangent line slope expression, differentiate the curve with respect to x:

set to find the x-coordinate at which the tangent line slope is -2. then that will also be the location of the normal.

to find y-coordinate, plug x=2 into the curve equation

so the point where this normal acts is (2,3). the slope of the normal is 1/2. therefore, the equation of the normal to the curve can be found using point-slope form, . this gives us

-13

step-by-step explanation:

f(x)=2x-5 for f(-4)

f(-4)   means let x=-4

f(-4) = 2(-4) -5

f(-4) =-8-5

      = -13