Find the equation of the tangent line to the curve y= 2x2 + x-1 at the point (5, 54).

y-54=21(x-5) or y=21x-51

Step-by-step explanation:

To find the equation of the tangent line, we first want to find the derivative of the equation.

f(x)=2x²+x-1           [Power Rule]

f'(x)=4x+1

Now that we have the derivative, we use (5,54) to find the slope.

f'(5)=4(5)+1            [multiply]

f'(5)=20+1              [add]

f'(5)=21

With our slope, we can plug it into point-slope form.

y-54=21(x-5)

We can also convert this to slope-intercept form.

y-54=21(x-5)          [distribute]

y-54=21x-105        [add both sides by 54]

y=21x-51

Now, we know the tangent line is y-54=21(x-5) or y=21x-51.

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: