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Please help solve this.
The answer also needs to be in long decimal form or fraction


Please Help Solve This The Answer Also Needs To Be In Long Decimal Form Or Fraction class=

Sagot :

Answer:   34/49

Work Shown

[tex]f(x) = \frac{g(x)}{h(x)}\\\\f'(x) = \frac{g'(x)h(x)-h'(x)g(x)}{( h(x) )^2}\\\\f'(4) = \frac{g'(4)h(4)-h'(4)g(4)}{( h(4) )^2}\\\\f'(4) = \frac{1*3.5-(-1)*5}{( 3.5 )^2}\\\\[/tex]

[tex]f'(4) = \frac{8.5}{12.25}\\\\f'(4) = \frac{850}{1225}\\\\f'(4) = \frac{34*25}{49*25}\\\\f'(4) = \frac{34}{49}\\\\[/tex]

Notes:

  • I used the quotient rule on the 2nd step.
  • It's not entirely clear, but I'm assuming that h(4) = 3.5 since this y value appears to be at the midpoint of y = 3 and y = 4.
  • The derivative helps us find the slope of the tangent line. In the case of linear functions, the derivative is just the slope of the line itself.
  • 34/49 = 0.69387755 approximately