Answer: 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.
