What is the equation of the line tangent to #f(x)=(2x^2 - 1) / x# at #x=1#?

Answer 1

y = 3x -2

Find the equation in slope-intercept form y = mx + c ,where m represents the gradient and c , the y-intercept. We require to find m and c. The value of f'(1) is the gradient of the tangent m , and f(1) will enable us to find c.

Begin by simplifying f(x). Divide terms on numerator by x.

#f(x)=(2x^2)/x-1/x=2x-x^-1#
now differentiate using the#color(blue)" power rule"#
#rArrf'(x)=2+x^-2=2+1/x^2#
and#f'(1)=2+1/(1)^2=3=m" (gradient of tangent)"#

hence partial equation is : y = 3x + c

now #f(1)=(2(1)^2-1)/1=1rArr" (1,1) is point on tangent"#

substitute x = 1 , y = 1 into partial equation to find c.

1 = 3(1) + c → c = -2

and equation of tangent at x = 1 is y = 3x -2 graph{(y-((2x^2-1)/x))(y-3x+2)=0 [-10, 10, -5, 5]}

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

The equation of the line tangent to f(x)=(2x^2 - 1) / x at x=1 is y = 3x - 1.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7