Graphical Zero Finding

library(mosaicCalc)

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Graphical Zero Finding

Misalnya, fungsi pemodelannya adalah $g(x)\equiv 1.7-0.85x+0.063x^2$ dan kamu mencari $x_0$ seperti $g(x_0)=3$.

f <- makeFun(1.7-0.85*x+0.063*x^2 ~ x)
Zeros(f(x) - 3 ~ x, bounds(x=-4:4))

## # A tibble: 1 × 2
##       x   .output.
##   <dbl>      <dbl>
## 1 -1.39 0.00000320

slice_plot(f(x) ~ x, bounds(x=-4:4)) %>%
  gf_hline(yintercept = ~ 3, color="red")

Situasi lain yang biasanya dibahas di sekolah menengah adalah membalikkan fungsi polinomial orde rendah. Kita akan mengerjakan masalah tersebut dalam proses menggunakan rumus kuadrat. Untuk menerapkan rumus kuadrat, kita perlu menempatkan soal ke dalam format standar, bukan $$1.7-0.85x+0.063x^2=3$$ Tetapi $$0.063x^2-0.85x-1.4=0$$

f <- makeFun(0.063*x^2-0.85*x-1.4 ~ x)
Zeros(f(x) - 0 ~ x, bounds(x=-4:4))

## # A tibble: 1 × 2
##       x   .output.
##   <dbl>      <dbl>
## 1 -1.48 -0.0000238

slice_plot(f(x) ~ x, bounds(x=-4:4)) %>%
  gf_hline(yintercept = ~ 0, color="red")

Referensi: Kaplan, Daniel. 2022. MOSAIC Calculus. GitHub Pages. https://dtkaplan.github.io/MC2/