find the slope of the tangent line at the given point. then, determine the equation of the tangent line in the form y = mx + b.
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find the slope of the tangent line at the given point. then, determine the equation of the tangent line in the form y = mx + b.
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Answer:
f'(x)=2x+3 --- derive
=2(1)+3 ---- evaluate the given point (1,5) x =1
=5 ---- the slope
tangent line formula:
y-y=m(x-x)
y-(5)=5(x-1)
y-5=5x-5
y=5x-5+5
y=5x <----- tangent line
__________________
f'(x)=x-2/x
=(x)(1)-(x-2)(1)/x² derive using quotient rule
=x-x+2/x²
=2/x²
=2/(1)²
=2 <--- the slope
y-(3)=2(x-1) evaluate
y-3=2x-2
y=2x-2+3
y=2x+1 the equation of the tangent line